Chapter 5, Problem 1RE

Solve each system by graphing.

$\begin{array}{l}2x+3y=-9\\ 3x+y=14\end{array}$

To determine

To graph: The system of equations $2x-3y=-9$, $3x+y=14$ and solve the equations.

Explanation of Solution

Given:

The system of equation as follows:

$\begin{array}{c}2x-3y=-9\\ 3x+y=14\end{array}$

Graph:

Sketch the graph using Ti83 applications:

Step 1:

Press the [Y=] key, then the equations for $y$ will appear there.

Step 2:

Express $2x-3y=-9$ in terms of $y$ and enter the equation in ${\text{Y}}_{\text{1}}$.

Step 3:

Press the [GRAPH] key to plot the graph.

Step 4:

Press the $\boxed{\text{TRACE}}$ key to plot the graph

It is evident in the graph that the pair $\left(3,5\right)$ is the point of intersection of the two lines.

So, the solution of the equations above is as follows:

$x=3$ And $y=5$.

Interpretation:

The solution of the equations is $x=3$ and $y=5$.